Crashes in Roswell, New Mexico, and flashing lights over New Jersey — for decades, people around the world have looked up at the skies and reported mysterious unidentified objects (UFOs).

But are these sightings signs of alien visitation? And are they truly unexplained?

A recent New York Times investigation found that the Pentagon had, for years, funded a program to answer just that question. The program found several reports of aircraft that seemed to travel at high speeds and have no signs of propulsion, the Times reported.

While the vast majority of UFO sightings, when investigated, have turned out to be the result of ordinary Earthly phenomena, such as weather balloons, flares or rockets, some still leave experts scratching their heads — and looking to the skies for little green men. From white Tic Tacs to flashing lights, here are some of the most mysterious UFO sightings out there. [7 Things Most Often Mistaken for UFOs]

Fighter pilot encounter

The Times investigation highlighted one of the most intriguing UFO sightings, which was captured on video. In 2004, two Navy F/A-18F fighter jets (also called Super Hornet or Hornet) encountered a mysterious flying object near San Diego, The New York Times reported. The object seemed to be traveling at high speeds, was surrounded by a glowing halo and was rotating as it moved. According to audio from the event, one of the fighter pilots exclaimed, “There’s a whole fleet of them,” the Times reported.

One of the Navy pilots who witnessed the bizarre event, Cmdr. David Fravor, recalled that the object looked like “a white Tic Tac, about the same size as a Hornet, 40 feet [12 meters] long with no wings,” Fravor told The Washington Post. As his plane approached the UFO, the mysterious object accelerated “faster than I’d ever seen anything in my life,” Fravor said.

Fravor, for his part, is convinced that the source of the object was extraterrestrial, he told The Washington Post.

French encounter

In 1981, a 55-year-old farmer in Trans-en-Provence, France, reported hearing a strange, high-pitched sound before seeing a flying saucer nearby. The lead-colored UFO took off almost immediately, he said.

What makes this sighting unique is that the farmer immediately contacted local police, who took soil and plant samples, according to a report of the incident. Experts from France’s UFO-investigating body, formerly called Groupe d’Études et d’Informations sur les Phénomènes Aérospatiaux Non-identifiés (GEPAN), said the chemical evidence was consistent with heating of the soil and pressure from a heavy object. They also found traces of zinc and phosphate and evidence of abnormalities in the plants nearby.

However, skeptics said the smooshed plants could have been caused by tires, and cars had been heard traveling in the area around the same time as the farmer’s sighting. Because there was a military base nearby, another explanation is that the French military was testing an experimental craft.

Sighting by retired astronaut

In general, some of the most reputable or credible sightings come from those who are in the skies all day long: pilots and members of the military. The National UFO Reporting Center (NUFORC) logged one such sighting in 2013, Vice reported. Late in the evening in 2013, the man, a former commercial pilot, fighter pilot and astronaut, was looking at the sky with his family in Athens, Texas, when he noticed what looked like an orange, glowing fireball.

“When I looked up into the sky, I saw a fairly large, orange, glowing orb moving rapidly overhead [at] right about 90 degrees of elevation,” the man reported to the NUFORC.

After a few minutes, a group of three similar objects followed the same flight path. Three minutes later, two more objects flew along that same route. The objects gave off no sound and seemed to glow from atmospheric heating, the man reported. He and his family attempted to record the objects using their iPhones, though the grainy, dark video was difficult to decipher, he said.

“They moved much faster than orbital satellites (International Space Station, for example) or airplanes, but much slower than meteors and did not change brightness as a meteor would upon entering the atmosphere,” the man said in his call. “I have no explanation for what we saw.”

Lights over Mount Shasta

Another report from the NUFORC came from an airline captain who was flying between Los Angeles and Portland, Oregon, when he noticed glowing blue lights over Mount Shasta in California that appeared much brighter than the stars typically do in the area.

“The two lights were approximately an inch apart in the windscreen and the size of normal stars,” the captain noted in a report. Then, “one of the ‘stars’ just dimmed out over about a 10-second time span followed by the other one dimming out completely in about 10 seconds also.”

The lights were stationary, so they were not falling stars or satellites, he said. [UFO Quiz: What’s Really Out There]

“We were flying in crystal-clear skies and were not flying though any clouds whatsoever. These two lights were not following the typical west-to-east orbital path as most satellites do and were just sitting there kind of like ships hiding in plain sight,” the captain reported to the NUFORC.

The lights also appeared to be far above the level of the plane, which was flying at 38,000 feet (11,580 m).

Not so U-FOs

For every unexplained sighting, there are dozens that turn out to be military flares, weird cloud formations, weather phenomena or elaborate hoaxes. For instance, GEPAN’s database suggests that only 7 percent of all supposed UFO sightings are truly unexplained.

In the 1940s, the U.S. Air Force began investigating UFO sightings, and that program, called Project Blue Book, logged more than 12,000 reported sightings before it was shuttered in 1969. Most of those Project Blue Book sightings were ultimately explained. While a few remained unexplained, the people involved in the program were skeptical that these cases were true alien sightings or completely unknown physical phenomena.

“If more immediate, detailed, objective data on the unknowns had been available, probably these, too, could have been explained,” a report in the Project Blue Book archive noted. However, the fact that human factors are involved — in particular, personal impressions and interpretations, rather than accurate scientific data — it’s likely impossible to eliminate all unidentified sightings, the report noted.